Superconformal algebras with quadratic nonlinearity

Defever, Filip; Troost, Walter; Hasiewicz, Zbigniew

doi:10.1016/0370-2693(91)90552-2

Cited by 11 publications

(26 citation statements)

References 16 publications

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“…First let us discuss briefly the case of gℓ(N|M). A real form of this algebra based on the compact superalgebra u(N|M) was constructed in [10]. The limit M = 0 coincides with the well known case based on su(N) × u(1) [2,3].…”

Section: The Case Of Sℓ(n + 2|n)mentioning

confidence: 87%

“…A convenient way of characterizing the quadratically nonlinear algebras is to specify the pair (g, ρ) where g is the (super) Lie algebra and ρ is the representation carried by the spin 3/2 currents. Various possibilities for this pair have been found [5][6][7][8][9][10] in addition to those in [2,3]. All the known cases are listed in Tables 1-3.…”

Section: Introductionmentioning

confidence: 99%

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BRST operator for superconformal algebras with quadratic nonlinearity

Khviengia¹,

Sezgin²

1994

Physics Letters B

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We construct the quantum BRST operators for a large class of superconformal and quasi-superconformal algebras with quadratic nonlinearity. The only free parameter in these algebras is the level of the (super) Kac-Moody sector. The nilpotency of the quantum BRST operator imposes a condition on the level. We find this condition for (quasi) superconformal algebras with a Kac-Moody sector based on a simple Lie algebra and for the Z 2 ×Z 2 -graded superconformal algebras with a Kac-Mody sector based on the superalgebra osp(N|2M) or sℓ(N + 2|N). †

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Section: The Case Of Sℓ(n + 2|n)mentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

BRST operator for superconformal algebras with quadratic nonlinearity

Khviengia¹,

Sezgin²

1994

Physics Letters B

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“…A simple inspection shows that this quotient algebra is none other than the Z 2 ×Z 2 graded extension of u(2|1) current superalgebra, u(2|1) SCA [24], which is some graded version of the u(3) KB SCA (the precise correspondence comes out with the choice k = −κ, m = 2, n = 1 in the general formulas of [24]). In contrast to the original N = 2 algebra with the spin 1/2 currents added, the quotient algebra does not contain the standard linear N = 2 SCA as a subalgebra; respectively, the N = 2 multiplet structure of the currents turns out to be lost.…”

Section: N = 2 U(2|1) Scamentioning

confidence: 99%

“…Appendix C: u(m|n) SCAs [24] in terms of currents This algebra includes Virasoro stress tensor T , 2n spin 3/2 bosonic currents, G a ,Ḡ a , 2m spin 3/2 fermionic currents, G b ,Ḡ b , a = m + 1, m + 2, . .…”

Section: )mentioning

confidence: 99%

“…It was demonstrated in [24,25,26] that new SCAs with quadratic nonlinearity, so-called Z 2 × Z 2 graded SCAs, can be obtained by combining both fermionic and bosonic spin-3/2 currents in the same osp(m|2n) or u(m|n) supermultiplet. The u(n) KB SCAs and the algebra W (2) 3 can be identified with Z 2 × Z 2 graded SCAs associated with the superalgebras u(n|0)and u(0|1), respectively § .…”

Section: Introductionmentioning

confidence: 99%

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N=2 affine superalgebras and Hamiltonian reduction inN=2 superspace

Ahn

Ivanov²,

Sorin³

1997

Commun.Math. Phys.

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We construct N = 2 affine current algebras for the superalgebras sl(n|n − 1)(1) in terms of N = 2 supercurrents subjected to nonlinear constraints and discuss the general procedure of the hamiltonian reduction in N = 2 superspace at the classical level. We consider in detail the simplest case of N = 2 sl(2|1)(1) and show how N = 2 superconformal algebra in N = 2 superspace follows via the hamiltonian reduction. Applying the hamiltonian reduction to the case of N = 2 sl(3|2)(1) , we find two new extended N = 2 superconformal algebras in a manifestly supersymmetric N = 2 superfield form. Decoupling of four component currents of dimension 1/2 in them yields, respectively, u(2|1) and u(3) Knizhnik-Bershadsky superconformal algebras. We also discuss how the N = 2 superfield formulations of N = 2 W 3 and N = 2 W (2) 3 superconformal algebras come out in this framework, as well as some unusual extended N = 2 superconformal algebras containing constrained N = 2 stress tensor and/or spin 0 supercurrents. *

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On asymptotic symmetries of 3d extended supergravities

Poojary¹,

Suryanarayana²

2019

J. High Energ. Phys.

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We study asymptotic symmetry algebras for classes of three dimensional supergravities with and without cosmological constant. In the first part we generalise some of the non-dirichlet boundary conditions of AdS 3 gravity to extended supergravity theories, and compute their asymptotic symmetries. In particular, we show that the boundary conditions proposed to holographically describe the chiral induced gravity and Liouville gravity do admit extension to the supergravity contexts with appropriate superalgebras as their asymptotic symmetry algebras. In the second part we consider generalisation of the 3d BMS computation to extended supergravities without cosmological constant, and show that their asymptotic symmetry algebras provide examples of nonlinear extended superalgebras containing the BMS 3 algebra.

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Superconformal algebras with quadratic nonlinearity

Cited by 11 publications

References 16 publications

BRST operator for superconformal algebras with quadratic nonlinearity

BRST operator for superconformal algebras with quadratic nonlinearity

N=2 affine superalgebras and Hamiltonian reduction inN=2 superspace

On asymptotic symmetries of 3d extended supergravities

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